OP, I am so sorry for your loss 
I do think yabu. I don't think anyone has the right to exclude anyone from a funeral. Everyone who loved her should be allowed at the funeral and should not be told they aren't welcome.
They aren't nosy neighbours, they are close relatives and I don't believe anyone should try to exclude them.
When my children's father died his widow was making all kind of requests about who could and who couldn't attend the funeral. She was grieving, she was trying to do what she thought he would have wanted. It was all down to raw grief and anger and trying to focus on something other than the deep loss. In the end, everyone who wanted to go went, it just didn't matter in the end, don't think she really noticed who was there and who wasn't. Ex step FIL wasn't happy when she said she wanted me to go in the funeral car with her and the children, I felt pulled by everyone's wishes, but on the day no one cared, none of it mattered, all that mattered was saying goodbye and coming together.
I would be devastated if my children couldn't go to a close relatives funeral, it's my job to know if they can handle it or not. Being upset is a part of life and not something they need protecting from unless the parents think it isn't appropriate.
That said, would I let my children attend a funeral when I was asked not to bring them? Probably not, I would talk it through but ultimately I wouldn't want to cause more upset at such an awful time, but I would be very hurt.
Again, I'm sorry for your loss OP 